Seismic reflection is a technique used to determine details of structures beneath the surface of the Earth. The resolution that may be achieved makes this technique the method of choice for oil exploration and mapping of subsurface rock structures. It is also applicable to experimental research that probes the fine structure within the Earth's crust and at the crust-mantle boundary.
The technique involves generating downward-propagating seismic waves in succession at a number of locations within the region being explored. A large number of receivers are positioned at intervals away from each source location and these receivers record the amplitudes (for example, in terms of pressure, displacement or its derivative) of seismic waves reflected back up to the surface from subsurface inhomogeneities over a period of time. The recorded waves are usually deconvolved, removing the effects of the source and receiver (which have their own response functions).
Reflection data typically have low amplitudes and are contaminated by multiple reflections and other kinds of noise. Various acquisition and processing techniques may be used to improve signal-to-noise ratios, such as averaging (stacking) of traces with the same midpoint, taking into account different distances between source and receiver, and discrimination of multiple reflections based on either their periodicity or wavefront angles which differ from the primary reflections. Further, the data may be correctly positioned in space by a process called migration, which moves dipping events into their correct position. When comparisons are made between two or more datasets over the same area, careful analysis between the amplitude, time and other attributes of the datasets may be made.
After the appropriate corrections, which may further include correction for other known environmental variables, the data are combined to provide a graphical representation of the subsurface inhomogeneities.
Seismic reflection data obtained by field experiments are then processed to obtain a three dimensional image of subsurface structures as described above. The three dimensions refer to the spatial dimensions “illuminated” by the seismic data. The vertical axis may represent depth or two-way vertical seismic wave travel time.
The amplitudes of reflected seismic waves are indicative of the subsurface reflection strengths, contaminated by noise. The reflection strength depends upon the reflection coefficient, which may be defined as a function of the relative contrasts of the elastic material properties of the subsurface layers.
The elastic properties of an isotropic, elastic medium are completely described by three parameters, for example the two elastic Lamé parameters and the density. Other parameterisations are possible, for example acoustic impedance, shear impedance and density. A third example is P-wave velocity, S-wave velocity, and density. The transformation between different sets of elastic parameters is well defined and straightforward.
In general, the elastic properties vary spatially. In order to explain the relationship between the elastic properties and the seismic data it may be convenient to imagine the subsurface as a stack of geological layers. The layer properties are described by the elastic properties of the rocks within the layers while the seismic data are related to the contrasts of the layer properties between successive layers. The seismic data are therefore suitable for interpreting subsurface layer structures since they image the boundaries between the layers.
Seismic inversion is defined herein as the process of transforming (inverting) seismic reflection data to elastic material properties, i.e. taking amplitudes (measurements of contrasts) and using them to infer physical layer properties. Numerous different seismic inversion techniques are known.
Over a period of time, certain types of rock, known as source rocks, will produce hydrocarbons. The produced hydrocarbons are then transferred to and stored in rocks known as reservoir rocks through various geological processes. During production of hydrocarbons in a subsurface region, the effective elastic material properties of the reservoir rocks change with production time, where production time is the fourth dimension in seismic 4D analysis. The changes of the effective elastic properties of the reservoir rocks may be caused by changes of the pore fluid saturations in the reservoir rocks, but also by pressure and temperature changes. Explained by a simple layer-based earth model concept, the properties of the reservoir layer are changed during production, implying changes in the reflectivity for the upper and lower reservoir interfaces. The measurements taken at a further seismic survey are related to the new contrasts at the boundaries between adjacent layers.
Reservoir changes are often inferred from a comparison of the seismic data (e.g. amplitudes of seismic waves reflected at interfaces bounding or within the reservoir) for different seismic surveys acquired at different stages of the production. A more direct interpretation can be based on difference data. Difference data are established by subtracting two time-separated seismic surveys covering a common part of the earth. The difference data, after the proper time-alignment during pre-processing, represent a spatial image of the changes of the relative contrasts between the two different acquisition times.
For a three dimensional seismic dataset, the classic inversion problem is to estimate the elastic material parameters from the three dimensional seismic data. A natural extension of 3D inversion to inversion of time-lapse seismic data (4D) is to invert the different 3D datasets separately by a known method, and then subtract the results to obtain the changes.
However, the reliability of 4D interpretations is difficult to assess, and are made by qualitative assessment. A full consideration of the uncertainties involved is important for making an accurate inference of the changes in the reservoir properties between the two seismic surveys. The results of such seismic analysis may be important in reservoir management in that the inferred reservoir properties are used to evaluate, for example, new drilling targets and future drainage strategies.
Seismic inversion provides quantitative estimates of the elastic reservoir properties. However, inversion of noisy seismic data is known to be a difficult and ill-posed procedure. An appropriate assessment of the uncertainties in 4D inversion data has not previously been possible.
Commercial time-lapse inversion techniques have become available, but only with brief descriptions of the methods. Some results have been published (Mesdag et al, 2003, Integrated AVO reservoir characterisation and time-lapse analysis of the Widuri field, 65th Mtg., Eur., Assn. Expl. Geophys., Extended Abstracts). Such methods apply separate inversions of the data with some constraint between the results, e.g. a common background model. The time-lapse change is then calculated from the change in inverted parameters. Sarkar et al, 2003, On the Inversion of time-lapse seismic data, 73rd Ann. Internat. Mtg.: Soc. Of Expl. Geophys., 1489-1492, mentions inversion of seismic differences, but provides no detail of the implementation. None of these inversion techniques provide uncertainty bounds on the results.